Write an expression that is equivalent to 3x3x3x3x3x3x3 ?!?!?!
The Correct Answer and Explanation is:
The expression ( 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 ) can be written as an exponent, which is the mathematical way to represent repeated multiplication of the same number.
In this case, since the number 3 is being multiplied by itself 7 times, you can express this as:
[
3^7
]
So, ( 3^7 ) is the correct expression that is equivalent to ( 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 ).
Explanation:
Exponentiation is a shorthand notation in mathematics for repeated multiplication of the same factor. In general, when you see an expression like ( a^b ), it means that the base ( a ) is being multiplied by itself ( b ) times. For example, ( 3^4 ) means ( 3 \times 3 \times 3 \times 3 ), or the number 3 multiplied by itself four times.
In your case, the expression ( 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 ) is equivalent to ( 3^7 ), because the number 3 is multiplied by itself a total of seven times.
The advantage of using exponents is that they simplify writing long strings of repeated multiplication. Instead of writing all the factors out, you can use just two numbers—the base (3) and the exponent (7)—to capture the entire operation.
If you were to evaluate this expression, you would calculate it step-by-step by multiplying the 3s together:
[
3^7 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 2187
]
Thus, ( 3^7 = 2187 ), but the exponential form is the more efficient way to express this repeated multiplication. This makes it particularly useful in both basic arithmetic and advanced areas like algebra and calculus.